Question

if vw = 18, find zw.

Explanation:

Step1: Recall the centroid theorem

The centroid of a triangle divides each median into a ratio of \(2:1\). That is, if a median is \(VW\), and \(Z\) is the centroid, then \(VZ:ZW=2:1\) and \(VW = VZ + ZW\).

Step2: Let \(ZW=x\), then \(VZ = 2x\)

Since \(VW=VZ + ZW\), and \(VW = 18\). Substitute \(VZ = 2x\) and \(ZW=x\) into the equation \(VW=VZ + ZW\). We get \(18=2x + x\).

Step3: Solve the equation for \(x\)

Combine like - terms: \(18 = 3x\). Divide both sides by \(3\): \(x=\frac{18}{3}=6\). So \(ZW = 6\).

Answer:

\(ZW = 6\)